Re: How many different unit fractions are lessorequal than all unit fractions? (infinitary)

On 10/08/2024 07:36 AM, Ross Finlayson wrote:

On 10/08/2024 12:30 AM, Moebius wrote:

Am 08.10.2024 um 09:29 schrieb Moebius:

Am 08.10.2024 um 02:38 schrieb Chris M. Thomasson:

On 10/7/2024 4:01 PM, Richard Damon wrote:

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I am allowing that an INFINITE being MIGHT be able to comprehend
something like an actual infinity. But this can not possibly be done
by a finite being.

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It can.
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This idiot should read Peter Suber's Infinite Reflections:

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"Perhaps it cannot be imagined but it can be conceived; it is not
reserved for infinite omniscience, but knowable by finite humanity..."
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"Conclusion
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Properly understood, the idea of a completed infinity is no longer a
problem in mathematics or philosophy. It is perfectly intelligible and
coherent. Perhaps it cannot be imagined but it can be conceived; it is
not reserved for infinite omniscience, but knowable by finite
humanity; it may contradict intuition, but it does not contradict
itself. To conceive it adequately we need not enumerate or visualize
infinitely many objects, but merely understand self-nesting. We have
an actual, positive idea of it, or at least with training we can have
one; we are not limited to the idea of finitude and its negation. In
fact, it is at least as plausible to think that we understand finitude
as the negation of infinitude as the other way around. The world of
the infinite is not barred to exploration by the equivalent of sea
monsters and tempests; it is barred by the equivalent of motion
sickness. The world of the infinite is already open for exploration,
but to embark we must unlearn our finitistic intuitions which instill
fear and confusion by making some consistent and demonstrable results
about the infinite literally counter-intuitive. Exploration itself
will create an alternative set of intuitions which make us more
susceptible to the feeling which Kant called the sublime. Longer
acquaintance will confirm Spinoza's conclusion that the secret of joy
is to love something infinite."
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Source: http://legacy.earlham.edu/~peters/writing/infinity.htm
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 > Well, us as finite beings know that there is not a largest natural
 > number... That right there is a basic understanding of the infinite:
 > Fair enough?
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Right.

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I associate Suber's with "material implication" thus a negative
connotation.
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http://legacy.earlham.edu/~peters/writing/infinity.htm
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Then he says about infinity that it's always looking like
Kant's "Sublime", then also that means Mirimanoff's "Extra-Ordinary".
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Then he says "there are paradoxes", and, no, there aren't.
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Then he's like "there's a completed infinity" and it's like,
well, yeah, obviously, then for something though like
the Sublime and Extra-Ordinary make that there are
always fragments and extensions of Infinity and yes
everyone knows that as Skolem/Louwenheim/Levy,
makes yet for more "Sublime" and "Extra-Ordinary"
that take some of the usual notions of "defining
omega a well-founded infinite inductive set" as
"Russell's a back-slider and his retro-thesis is, too".
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So, infinitary reasoning disambiguates then via a
deconstructive account _resolves_ paradoxes, not
merely wishing them away, then wishing them away
the Russell-ian way is a conceit to something that
the extra-ordinary can arrive at _is even more
complete and replete than just 'merely' complete_,
the infinity.
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I associate Mirimanoff with a positive connotation.
As in 'not eventually or ultimately wrong'.
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>
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Now, that sort of paper reflects some reasonings
that come along in the usual course of mental maturity
about infinity, and of course of a study of it,
yet as soon as "Sublime" is introduced, and "Extra-
Ordinary", it's beyond Suber's fundamentally closed
and Russell-ian account.
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"Truths", of mathematical infinities.
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The idea that Frege came up with "material implication"
I rather disagree, and nobody "needs" material implication
to prove _anything_ of fact, and "direct implication" is
what _anybody_ means when they say "implies".
Or, "anybody who buys or shills material implication
is a fool or a fraud, and a moon of green cheese".
The moon is not made of green cheese. And: material
implication might: or might not, materially imply.
The "material implication" is one of the things I
find _most_ objectionable, as with regards to its
misnomer in "classical logic", which is instead,
a "quasi-modal" logic, and as covered here many times,
is neither modal, monotonic, nor brings entailment,
except in its own little closed graphical sense of ~p v q,
which wastes space in the tableau with non-material things
that are not implied and under any change of things which
results any change of conditions, is exactly _not_ modal,
in "the modality", the temporal modality.
Nobody "needs" material implication to do logic,
any need _not_ it to do modal logic, and many
look to relevance logic as much more classical,
and classical logic does _not_ have quasi-modal material implication.